Avery Bradley is much closer to Tony Allen than he is to Gabe Pruitt. Undersized, defense first, athletic guard without great handles and good mid range game. While Bradley lacks the strength to guard 3's like Tony, he already has a much better offensive game. He's only 20 and has a ton of upside. Avery can be a top point guard in this league working with Doc Rivers and Rajon Rondo.
I disagree that Bradley has a better offensive game than Allen right now. He is a (slightly) better shooter at the moment, but Tony has always been significantly better at getting to the basket and finishing.
My biggest problem/worry about Bradley's ability to be a quality NBA player is that he has yet to show the ability to use a quick first step on dribble drives, and to finish strong at the basket. For a player who relies on their athleticism, this is a real key. When he was not being guarded by the Knick's matadors in that last game, he was absolutely terrible at getting separation, and kept resorting to weak floaters because he could not beat his man.
Allen on the other hand has always had that strong first step. He has his issues offensively, but if you get him in position for a 2 dribble drive, he is very hard to defend.
Unless Bradley can learn that (and this is footwork he should have learned in middleschool or earlier), he is going to be incredibly easy to defend in the NBA, and his cieling will likely drop to no more than a defensive specialist at best.